Time-Varying Formation for Second Order Nonlinear Multi-agent System with Switching Topology and Time Delay

In this paper, time-varying formation problem for nonlinear second order multi-agent system in existence of switching directed topology and time delay is investigated. First, we design an reduced-order extended state observer (ESO) to estimate the nonlinear dynamics, then we construct a time-varying formation protocol. After that we prove that the ESO estimation error can be arbitrarily small. Sufficient conditions for the system to form the desired formation are obtained by using Lyapunov-Krasovskii functional approach and Linear Matrix Inequality (LMI) technique. Then we present an explicit expression of the time-varying formation reference function. Finally, we use numerical simulation to verify the validity of the theoretical results.